Abstract
In this article, we establish an almost sure invariance principle for the capacity
and cardinality of the range for a class of α-stable random walks on the integer
lattice Zd with d > 5α/2 and d > 3α/2, respectively. As a direct consequence, we
conclude Khintchine's and Chung's laws of the iterated logarithm for both processes.
and cardinality of the range for a class of α-stable random walks on the integer
lattice Zd with d > 5α/2 and d > 3α/2, respectively. As a direct consequence, we
conclude Khintchine's and Chung's laws of the iterated logarithm for both processes.
| Original language | English |
|---|---|
| Article number | arXiv:1910.09831v1 |
| Number of pages | 16 |
| Journal | arXiv.org e-Print archive |
| Publication status | Published - 2019 |
Keywords
- The range of a random walk
- Capacity
- An almost sure invariance principle
- The law of the iterated logarithm
ASJC Scopus subject areas
- Mathematics(all)